Question

25. Find the value of the side marked y in the diagram below? 10cm 8cm (a) 7cm (b) 8cm (c) 14cm (d) 6cm (e) 15cm Y​

Answer 1

d

Explanation:

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other two sides , that is

y² + 8² = 10²

y² + 64 = 100 ( subtract 64 from both sides )

y² = 36 ( take square root of both sides )

y =
`√(36)` = 6 cm

Answer 2

(d) 6 cm

Explanation:

As the given triangle is a right triangle, we can use Pythagoras Theorem to calculate the side marked y.

Pythagoras Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

`\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}`

From inspection of the given triangle:

• a = 8 cm
• b = y
• c = 10 cm

Substitute these values into the formula and solve for y:

`\begin{aligned}a^2+b^2&=c^2\\\implies 8^2+y^2&=10^2\\64+y^2&=100\\64+y^2-64&=100-64\\y^2&=36\\√(y^2)&=√(36)\\y&=6\end{aligned}`

Therefore, the length of the side y is 6 cm.