## ABC is a right triangle .b is right angle. Ab is 7 units more than BC if area of a triangle is 60 square units find the length of ab and BC

Question

ABC is a right triangle .b is right angle. Ab is 7 units more than BC if area of a triangle is 60 square units find the length of ab and BC and the length of AC

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2 weeks 2021-11-24T21:52:27+00:00 2 Answers 0 views 0

1. ## GIVEN:

• AB is 7 units more than BC.
• Area of the triangle is 60 sq. units.

## TO FIND:

• What is the length of AB, BC and AC ?

## SOLUTION:

Let the side BC be ‘x’ units

We have given that, AB is 7 units more than BC.

So, let side AB be ‘x + 7 units

To find the area of the triangle, we use the formula:-

### ❮ AREA = ❯

According to question:

➸ 60 =

60 2 = x² + 7x

120 = x² + 7x

0 = x² + 7x –120

0 = x² + (15–8)x –120

0 = x² + 15x –8x –120

0 = x(x + 15) –8(x + 15)

0 = (x –8)(x + 15)

x = 15 ❱ (Neglected)

❰ x = 8 ❱

• x = BC = 8 units
• x + 7 = AB = 8+7 = 15 units

To find the length of AC, we apply the Pythagoras theorem

### ⠀⠀ ❰ H² = P² + B² ❱

Where,

• H = Hypotenuse
• P = Perpendicular
• B = Base

According to question:

➨  (AC)² = (AB)² + (BC)²

AC² = 15² + 8²

AC² = 225 + 64

AC² = 289

AC = √289

AC = 17 units ❭

Hence, the length of AB, BC and AC is 15, 8 and 17 units respectively.

## ______________________

LET BC BE X AND AB= X+7

SO area of rt angle triangle = 1/2 * product of legs=

here 1/2 * x* (x+7)= 60

on simplifying, we get, x^2 + 7x- 120= 0