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What is the answer to this?

What is the answer to this?-example-1
User Krishnab
by
8.2k points

1 Answer

3 votes

Explanation:

what is missing is the definition that QS is the height and therefore standing at a right angle (90°) at PR.

then this can be solved.

we use Pythagoras

c² = a² + b²

c being the Hypotenuse (the side opposite of the 90° angle), a and b are the legs.

let's start with the triangle PQS.

21² = 15² + QS²

441 = 225 + QS²

QS² = 216

QS = sqrt(216) = sqrt(36×6) = 6×sqrt(6) = 14.69693846...

now for triangle QSR

(5x - 16)² = (3x - 4)² + QS²

25x² - 160x + 256 = 9x² - 24x + 16 + 216

16x² - 136x + 24 = 0

2x² - 17x + 3 = 0

the solution to a quadratic equation

ax² + bx + c = 0

is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = (17 ± sqrt(17² - 4×2×3))/(2×2) =

= (17 ± sqrt(289 - 24))/4 = (17 ± sqrt(265))/4

x1 = (17 + 16.2788206...)/4 = 8.319705149...

x2 = (17 - 16.2788206...)/4 = 0.180294851...

but using x2 in side lengths 3x - 4 or 5x - 16 gives us negative side lengths. that does not make any sense for actual side lengths.

so, x1 is our solution :

x = 8.319705149...

User Leymannx
by
8.3k points

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