Question

The vertical of three squares are joined to form a right triangle , what is the area of the largest square

A- 25cm^2
B- 202,500cm^2
C- 34cm^2
D- 43cm^2

Answer 1

Check the picture below.

Answer 2

43cm²

Explanation:

let's first consider the area of a square.

the area is L² which means all sides are equal so we take the length times the breadth which is both equal because like we said all sides are equal.

so to find the side of the square using the area, we take the square root of both of the area.

`√(25) = 5`

and also

`√(18) = 4.2`

so we have the height of the triangle as 5cm and the base is 4.2cm.

now, from the triangle, since we have two sides and it's a right-angled, we can use Pythagoras' formula.

`\sqrt{ {5}^(2) + {4.2}^(2) } = 6.53cm`

so the side 6.53cm is also the same side as the largest triangle. Since it's a square, all sides are equal. So we find the area of the largest triangle by using the formula

Area = L²

Area = 6.53²

Area = 42.6cm

the nearest cm square

Area = 43cm²