Question

The height of a triangle is 7cm less than its base if the hypotenuse is 13cm form the quadratic equation to find the base of the triangle.

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Answer 1

Given that The altitude of a right triangle

is 7 cm less than its base:

Altitude is = x-7 cm

Given that hypotenuse = 13cm. Applying Pythagoras theorem,

base2+ altitude2 = hypotenuse2 plug the values we get

x2+ ( x-7)2 = 132

x2+ x2+ 49 – 14 x = 169

2 x2 – 14 x + 48 – 169 = 0

2 x2 – 14 x - 120 = 0

Divide by 2 to both side to simplify it

x2 – 7 x - 60 = 0

x2 - 12 x + 5 x - 60 = 0

x ( x - 12) + 5 ( x- 12) = 0

(x- 12)( x + 5) = 0

x - 12 = 0 or x+5 = 0

x= 12 or x = -5

length can not negative so that x can not

equal to - 5

base x = 12cm altitude = 12 - 7 = 5cm

$<marquee behaviour-move> <font color="lime"> <h1>sɴᴇʜᴀsʜɪsʜ</ ht> </marquee>$

Answer 2

${\tt{\green{\underline{\underline{\huge{Question}}}}}}$

The height of a triangle is 7cm less than its base if the hypotenuse is 13cm form the quadratic equation to find the base of the triangle.

${\tt{\red{\underline{\underline{\huge{solution:}}}}}}$

Let base = x cm and height = (x - 7) cm

Hypotenuse = 13 cm

By Pythagoras theorem,

${x^{2}+ (x - 7)^{2} = 132^{2}}$

$\bold\red{x^{2}+ 49 + x^{2} - 14x = 169}$

$2x^{2} - 14x - 120 = 0$

x² - 12x + 5x - 60 = 0

x( x - 12) + 5 (x - 12) = 0

0 (x - 12) (x + 5) = 0

x - 12 = 0 or x + 5 = 0

x-12 or x=-5 (rejecting)

The other two sides are 12 cm and 5 cm.

hope it's helps