Question

The altitude of right triangle is 7cm less than its base. If the hypotenuse is 13cm, Find the other two side.​

Answer 1

Answer:

Base=12 and Altitude=5

Answer 2

✬ Base = 12 cm ✬

✬ Altitude = 5 cm ✬

Step-by-step explanation:

Given:

• Altitude of a right triangle is 7 cm less than its base.
• Measure of hypotenuse is 13 cm.

To Find:

• What is the measure of altitude & base of right triangle ?

Solution: Let the meaure of base of right triangle is x cm. Therefore

➟ Measure of altitude = 7 cm less than x

➟ Altitude = (x – 7) cm

Now in right angled triangle we have

• Hypotenuse (h) = 13 cm
• Base (b) = x cm
• Altitude (p) = (x – 7) cm

Applying Pythagoras Theorem in right triangle

★ Pythagoras Theorem: H² = B² + P² ★

$\implies{\rm }$ (13)² = (x)² + (x – 7)²

[ Using, (a – b)² = a² + b² –2ab ]

$\implies{\rm }$ 169 = x² + (x² + 7² – 2 $\times$ x $\times$ 7)

$\implies{\rm }$ 169 = 2x² + 49 – 14x

$\implies{\rm }$ 0 = 2x² – 14x + 49 – 169

$\implies{\rm }$ 0 = 2x² – 14x – 120

$\implies{\rm }$ 0 = 2(x² – 7x – 60)

$\implies{\rm }$ 0 = x² – 7x – 60

[ By middle term splitting ]

➱ 0 = x² – 12x + 5x – 60

➱ 0 = x (x – 12) + 5 (x – 12)

➱ 0 = (x – 12) (x + 5)

➱ x = 12 or x = –5

Since, the measure of side cannot be negative.So the base of triangle will be x = 12 cm.

∴ Altitude = (x – 7) = 12–7 = 5 cm.

_____________________

★ Verification ★

➨ 13² = 12² + 5²

➨ 169 = 144 + 25

➨ 169 = 169

[ Verified ]