Question

plssss help!!!! Right triangle RST is drawn below. A square is drawn on to each leg of the triangle, and a square is drawn onto the hypotenuse of the triangle. The area of square A is 25 cm² . The area of square B is 144 cm². Determine the length in centimeters of x, the hypotenuse of the right triangle.O 13 cmO 17 cm O 169 cmO 119 cm

Answer 1

the hypotenuse of the right angled triiangle = x = 13cm (option A)

Step-by-step explanation:

Area of B = 144cm²

Area of a square = length²

length = √Area of a square

shape of B is a square, hence the length of B:

the length of one of the side of B = √144 = 12cm

Area of A = 25cm²

shape of A is a square

the length of one of the side of A = √25 = 5cm

Triangle is a right angled-triangle

From the diagram, the length of the side of B = opposite = 12cm

The length of the side of A = adjacent = 5cm

The length of the third square marked x = hypotenuse

Using pythagoras' theorem:

Hypotenuse² = opposite² + adjacent²

x² = 12² + 5²

x² = 144 + 25

x² = 169

x = √169

x = 13cm

Hence, the hypotenuse of the right angled triiangle = x = 13cm (option A)