Question

The area of a right triangle is 96 cm . If its base exceeds the altitude by 4 cm then calculate the perimeter of the triangle.

Answer 1

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I hope you don’t need the method to find the perimeter.

Answer 2

✪ANSWER✪

• Perimeter of the right triangle is 48 cm.

★EXPLAINATION★

☆GIVEN☆

• Area of triangle is 96 cm².
• Base exceeds the altitude by 4 cm.

☆TO FIND☆

• Perimeter of the triangle.

☆CALCULATION☆

✯ʙᴀsᴇ ᴀɴᴅ ᴀʟᴛɪᴛᴜᴅᴇ

Let x be the altitude and x + 4 be the base of the right triangle.

area = $\frac{1}{2}\times (base)\times (altitude)$

$⇒96 = \frac{1}{2}\times (x+4)\times (x)$

$⇒192 = x² + 4x$

$⇒ x² + 4x - 192 = 0$

$⇒ x² + 16x -12x - 192 = 0$

$⇒ x(x + 16) -12(x + 16) = 0$

$⇒ (x + 16)(x - 12)= 0$

$⇒ x = -16 or 12$

Since altitude cannot be negative

$⇒ x = 12$

So, base = x + 4 = 16 cm

Altitude = x = 12 cm

✯ʜʏᴘᴏᴛᴇɴᴏᴜs

Hypotenous² = base² + altitude²

⇒Hypotenous² = 16² + 12²

⇒Hypotenous² = 400

⇒Hypotenous² = 20

✯ᴘᴇʀɪᴍᴇᴛᴇʀ

Perimeter = Base + Altitude + Hypotenous

⇒ Perimeter = 16 + 12 + 20

⇒ Perimeter = 48 cm