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

Answer 1

Answer:

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

quadratic so, (x-8)(x+15)= 0

so x= -15 or 8 length isnt -ve

AB =8 & BC= 15

BY PYTHAGORAS THEOREM, AC = 17 '

PLS MARK BRAINLIEST

Answer 2

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 = $\bf{\dfrac{1}{2} \times b \times h}$ ❯ 

According to question:-

➸ 60 = $\sf{\dfrac{1}{2} \times x \times x + 7}$

➸ 60 $\times$ 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. ❞

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