Question

I can't do it I stuck in 2x
$2 {x | }^{2} - 60x - 120 = 0$
​

Answer 1

Let the Length of the base be : B

Given : Altitude of the Right angled triangle is 7 cm less than its base

$:\implies$  Length of Altitude = (B - 7) cm

Given : Length of the Hypotenuse = 13 cm

We know that, According to Pythagorean Theorem :

★  (Hypotenuse)² = (Altitude)² + (Base)²

$:\implies$  13² = (B - 7)² + B²

$:\implies$  B² + 49 - 14B + B² = 169

$:\implies$  2B² - 14B - 120 = 0

$:\implies$  B² - 7B - 60 = 0

$:\implies$  B² - 12B + 7B - 60 = 0

$:\implies$  B(B + 7) - 12(B + 7) = 0

$:\implies$  (B - 12)(B + 7) = 0

$:\implies$  B = 12   (or)   B = -7

As Length cannot be Negative $:\implies$ B ≠ -7

$:\implies$  B = 12

$:\implies$  Base of the Right angled triangle = 12 cm

$:\implies$  Altitude of the Right angled triangle = 5 cm