## QN07: The altitude of a right Ais 7cm less than its base. If the hypotenuse is 13cm. find the other two sides (7cm)​

Question

QN07: The altitude of a right Ais 7cm less than its base. If the hypotenuse is 13cm.
find the other two sides (7cm)​

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21 hours 2021-10-13T08:57:31+00:00 2 Answers 0 views 0

1. ## Solution

Let the base of right triangle be x the altitude be (x – 7)

Hypotenuse = 13 cm

(hypotenuse)²=(base)²+(perpendicular)²

(13)² = (x)² + (x – 7)²

169 = x² + x² + (7)² – 2 × x × 7

169 = 2x² + 49 – 14x

169 – 49 = 2x² – 14x

120 = 2x² – 14x

2x² – 14x – 120 = 0

2(x² – 7x – 60) = 0

x² – 7x – 60 = 0

x² + 7x – 12x – 60x = 0

x(x + 7) – 12(x + 7) = 0

(x + 7)(x – 12) = 0

______________

(x + 7) = 0

x = – 7

____________

(x – 12) = 0

x = 12

______________

Base = x = 12 m

Altitude = (x – 7) = (12 – 7) = 5m

2. ### Given

The altitude of a right is 7cm less than its base. If the hypotenuse is 13cm.

### Find out

Find the other two sides

### Solution

Let the base of right triangle be x the altitude be (x 7)

• Hypotenuse = 13 cm

According to the Pythagoras theorem

(hypotenuse)²=(base)²+(perpendicular)²

➟ (13)² = (x)² + (x – 7)²

Apply identity :

(a b)² = + 2ab

➟ 169 = x² + x² + (7)² – 2 × x × 7

➟ 169 = 2x² + 49 – 14x

➟ 169 – 49 = 2x² – 14x

➟ 120 = 2x² – 14x

➟ 2x² – 14x – 120 = 0

➟ 2(x² – 7x – 60) = 0

➟ x² – 7x – 60 = 0

Splitting middle term

x² + 7x – 12x – 60x = 0

➟ x(x + 7) – 12(x + 7) = 0

➟ (x + 7)(x – 12) = 0

Either

➟ (x + 7) = 0

➟ x = – 7

Or

➟ (x – 12) = 0

➟ x = 12

Length can’t be in negative

Hence,

• Base = x = 12 m
• Altitude = (x – 7) = (12 – 7) = 5m 