Question

a right triangle has an area of 20 square inches. The square of the hypotenuse is 116. find the lengths pf the legs pf the triangle.

Answer 1

is it correct to use the base measurement as sqrt166 which is 12.88

Answer 2

it's actually 116

Answer 3

It's 116 isn't it? The hypotenuse squared. So \[\large 116 = base^2+height ^2\]

Answer 4

sorry typo.

Answer 5

@Kkutie7 what happened to your equation?

Answer 6

humm?

Answer 7

oh I deleted it! I'm sorry. I'm kind of out of it right now. I basically solved for one component and substituted into the other equation.

Answer 8

\[a ^{2}+b ^{2}=116\]

Answer 9

\[116=base^{2}+height^{2}\]
\[20=\frac{1}{2}base*height\]

Answer 10

\[(\frac{ 40 }{ b})^{2}+b ^{2}=116\]

Answer 11

20=\[\frac{ 1 }{2 }base \times height\]
40=\[base \times height\]

Answer 12

\[\frac{ 40 }{ base }=height\]

Answer 13

and then i sub the height from this equation into the pythagorean theorem equation?

Answer 14

\[116=\left(\begin{matrix}40 \\ base\end{matrix}\right)^{2}+b ^{2}\]

Answer 15

but what do i do next?

Answer 16

Multiply both sides (every term) by b^2