the legs of a right Triangle are in ratio 3 : 4 and its area is is 101 4 CM square. Find its hypotenuse Question the legs of a right Triangle are in ratio 3 : 4 and its area is is 101 4 CM square. Find its hypotenuse in progress 0 Math Elliana 1 month 2021-08-17T05:38:11+00:00 2021-08-17T05:38:11+00:00 2 Answers 0 views 0

## Answers ( )

Figure :- Refers to the attachment✴ The legs of a right triangle are in ratio 3 : 4 and its area is is 1014 cm². Find its hypotenuse.

➡ The hypotenuse of Triangle is 65 cm.

Given:-To Find:-Calculation:-Let the leg of the triangle be x

So it’s sides 3:4 are equal to 3x and 4x .

According to the question,We know the,

Area of right angletriangle=×base×hieght.➝ 1014 = × 3x × 4x

➝ 1014 × 2 = 3x × 4x

➝ 2028 = 12x²

➝ = x²

➝ x² =

➝ x² = 169

➝ x =

➩

x = 13 cmUsing x finding the sides oftriangle,Here , We have a right triangle,applying Pythagoras theorem.

✒states the sum of the square of two sides namely, perpendicular & base is equals to the square of its hypotenuse.Pythagoras theorem➤

Hypotenuse ² = P² + B²➠ Hypotaneuse² = 39² + 52²

➠ Hypotaneuse² = (39×39) + (52×52)

➠ Hypotaneuse² = 1521 + 2704

➠Hypotaneuse =

➙

Hypotaneuse= 65 cm.⍈

Hence,The hypotenuse of the triangle is 65 cm._____________________________________Correct Question:The

length of two short sidesof a right Triangle is in ratio 3:4 and its area is 1014 CM square. Find its hypotenuse.Solution:-

Given:Let, the side i.e

Basebe 3x cmAnd

Perpendicular (height)be 4x cmArea of the triangle = 1014 cm sq.∴ x = 13

So, Base = 3x = 39cm

And Perpendicular(height) = 4x = 52cm

So, by using Pythagoras theorem,⇒ Hypotenuse² = (39)² + (52)²

⇒ Hypotenuse² = 1521 + 2704

⇒ Hypotenuse² = 4225

⇒ Hypotenuse =

⇒ Hypotenuse = 65cm

Hence,

The Hypotenuse of the right-angled triangle is 65cm.