Question

The area of a right triangle is 180 m². The height of the right triangle is 40 m. What is the length of the hypotenuse of the right triangle?

Answer 1

Assuming the height is one of the legs, the other leg is `9` and the hypotenuse is `41`.

Explanation:

It's not clear if the height is one of the legs or the altitude to the hypotenuse.

Either way we have `A =1/2 b h` or `b={2A}/h=2cdot(180)/40=9` m.

If `h=40` is the height to the hypotenuse, the hypotenuse is `9` m and we're done. Let's assume `h=40` is one of the legs so `b=9` is the other leg so

`c^2= h^2 + b^2 = 40^2+9^2=1681`

`c = 41`

Answer 2

`41 m`

Explanation:

`"In the right"" triangle ABC`

`:.angle B= 90^@` `"given"`

`:.BC=40 m= "height given"= opposite`

`:."Area of a triangle"=1/2 base xxh=180 m^2`

`:."1/2basexx40=180`

`:.1/2 base=180/40`

`:.1/2 base=4.5 m`

`:.base=9m=AB=adjacent`

`:.(opposite)/(adjacent)=(BC)/(AB)=40/9=tan angle A=4.444444444`

`:.angle A=77^@19'11''`

`:."AC= hypotenuse",(AC)/(BC)=sec 77^@19'11''=4.555555556`

`:.AC=sec 77^@19'11''xx 9=41 m=" hypotenuse"`