Can you find the area of the right triangle? | (Algebra) | #math #maths | #geometry

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Can you find the area of the right triangle? | (Algebra) | #math #maths | #geometry

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[yalchingedikgedik]

Very nice and enjoyable
I like these exercises
Thanks Sir for your efforts
With my respects ❤❤❤

[skverma]

Sir, there is no need to calculate "a" and "b" seperately.
a^2+b^2=148^2
(a+b)^2=188^2
2ab= (188+148) (188-148)
2ab = 336×40
1/2 ab= 3360 units

[turbavykas]

a*a + 2ab+ b*b = 188*188; a*a+b*b=148*148 (right triangle rule) so we get 2ab=188*188-148*148 area = ab/2 = (188*188-148*148)/4

[AmirgabYT]

a²+b²=21904
a+b=188

ab/2=?

(a+b)²=35344
a²+2ab+b²=35344
21904+2ab=35344
2ab=13440
ab/2=3360

S=3360 square units

[jkwwuxd]

(a+b)^2 = a^2 + b^2 + 2ab => (148)^2 + 2ab = (188)^2 => 2ab = (188)^2 - (148)^2 => ab = (((188+148)(188-148)))/2 => ab = 336×20 => area of the triangle=> 336×10 = 3360 u^2

[vcvartak]

a^2+b^2=(148)^2
a^2+b^2+2ab =(188)^2
ab/2=(188-144)*(188+144)/4 . a and b aren't needed

[devondevon]

3, 360
The perimeter of the triangle = (a+ b) or 188 + 148 = 336
The factors of 148 = 2, 37, 74
The Pythagorean triplet, 12, 35, 37 and a sum of 84
84 * 4 = 366
The triangle is a 12-35-37 right triangle scaled up by 4.
Hence, the bases are 48 and 140
Hence, area = 24 * 140 = 3, 360

[Alishbavlogs-bmip]

Wow very beautiful sharing thank you for sharing 💘💘💘

[ashutoshkumardalei]

(a+b)^2= a^2 +b^2+2ab
a^2+b^2=148^2
By solving these 2 equations we get (ab) as 6720
Then for area we can do ab/2 or 6720/2 = 3360.

[erwinkurniadi]

area = ½(a.b)
a²+b² = 148²
(a+b)² - 2ab = 148²
188² - 148² = 2ab
ab = (188² - 148²)/2
area = ½(188² - 148²)/2 = 3360

[alexniklas]

a^2+b^2=148^2;
(a+b)^2=188^2;
2ab= 188^2-(a^2+b^2);
2ab= 188^2-148^2= 13440;
S= 2ab/4=13440/4=3360

[ChuzzleFriends]

△ACB is a right triangle.
a² + b² = c²
a² + b² = 148²
= 21904
It is given that a + b = 188.
(a + b)² = a² + 2ab + b²
188² = c² + 2ab
35344 = 21904 + 2ab
2ab = 13440
(2ab)/4 = 13440/4
(ab)/2 = 3360 (This is the area formula in terms of a & b)
So, the area of the triangle is 3360 square units.

[prossvay]

a+b=188 (1)
a^2+b^2=(148)^2=21904
{1) (a+b)^2=(188)^2
a^2+2ab+b^2=35344
2ab=35344-21904
ab=6720 (2)
(1) b=188-a
(2) a(188-a)=6720
a^2-188a+6720=0
a=140 ; a=48
b=48 ; b=140
Area of the triangle=1/2(140)(48)=3360 square units.❤❤❤

[MrPaulc]

148^2 = 21, 904
Try a^2 + b^2 100 and 88 due to 10, 000 + 7, 744 respectively = 17, 744.
As a^2 + b^2 needs to be higher, the numbers need to be farther apart, and they can't both be odd. As one needs to be even, both must be because they add up to 188.
As c^2 ends in a 4, and even square numbers must end in 0, 4, or 6, that eliminates many of the possibilities.
Try 140 and 48
19, 600 + 2, 304
That seems to be the solution to side lengths as 140 + 48 = 188 and 19, 600 + 2, 304 = 21, 904.
Area is (140*48)/2
7*48=336, so 3, 360 un^2
Probably not the type of solution you seek, as a fair chunk of it (which I didn't show) was using maths logic to eliminate possible solutions, but I suppose my way is valid too.
Thank you.

[rotreal]

We can just use heron's formula, because you need to add up all 3 sides to get the semiperimeter, which in this case they've already provided

[unknownidentity]

Let's find the area:
.
..
...
....


Since the triangle is a right triangle, we can apply the Pythagorean theorem:

AC² + BC² = AB²
AC² + (188 − AC)² = 148²
AC² + 35344 − 376*AC + AC² = 21904
2*AC² − 376*AC + 13440 = 0
AC² − 188*AC + 6720 = 0

AC = 94 ± √(94² − 6720) = 94 ± √(8836 − 6720) = 94 ± √2116 = 94 ± 46

So we have two possible solutions:

AC = 94 + 46 = 140 ⇒ BC = 188 − AC = 188 − 140 = 48
AC = 94 − 46 = 48 ⇒ BC = 188 − AC = 188 − 48 = 140

In both cases the area turns out to be:

A = (1/2)*AC*BC = (1/2)*140*48 = 3360

Best regards from Germany

[santiagoarosam]

a+b=188--->a=188-b---> (188-b)²+b²=148²---> b=48 ---> a=140---> a*b/2=140*48/2= 3360 ud².
Gracias y saludos.

[Bozhidar_Delchev]

a^2 + b^2 = c^2 => (a+b)^2 - 2ab = c^2 => 188^2 - 4S = 148^2 => 4S = (188-148)(188+148) => S = 3360

[cosmolbfu]

a^2 + b^2 = 148^2 ***1
(a+b)^2 = 188^2 ***2

2-1
2ab = (40)(336)
ab/2 = 3360 = A

[SrisailamNavuluri]

148=4×37
188=4×47
37=36+1÷6^2^+1^2
One side is 2×6=12
37^2-12^2=49×25
3rd side is 35.
Area =16×1/2×(12×35)=16×6×35
=16×210=3320 sq units