Question

If two sides of a right-angled triangular park be 24 m and 10 m respectively, find the lens
its hypotenuse.
In a right A XYZ right angled at Y, XZ = 37 m, XY = 12 m. Find YZ.
​

Answer 1

$\bf{\huge{\underline{\boxed{\sf{\green{Answer:}}}}}}$

For first Δ ABC,

$\bf{\underline{\sf{\red{Given:}}}}$

• Side 1 = AB = 24 m
• Side 2 = BC = 10 m

$\bf{\underline{\sf{\red{To\:find\::}}}}$

• Length of the hypotenuse = AC

$\bf{\underline{\sf{\red{Solution:}}}}$

Δ ABC is a right angled triangle.

m$\angle$ABC = 90°

•°• By Pythagoras Theorem,

Hypotenuse² = ${S_1\:^2}$ + ${S_2\:^2}$

Hypotenuse ² = AB² + BC²

Hypotenuse ² = 24² + 10²

Hypotenuse ² = 576 + 100

Hypotenuse ² = 676

Hypotenuse = $\sqrt{676}$

Hypotenuse = 26 m

Length of the hypotenuse, AC = 26 m

In Δ XYZ,

$\bf{\underline{\sf{\red{Given:}}}}$

• Side 1 = XY = 12 m
• Hypotenuse = XZ = 37 m

$\bf{\underline{\sf{\red{To\:find:}}}}$

• Length of Side 2 = YZ

$\bf{\underline{\sf{\red{Solution:}}}}$

Δ XYZ is a right angled triangle.

m$\angle$XYZ = 90°

•°• By Pythagoras Theorem,

Hypotenuse² = ${S_1\:^2}$ + ${S_2\:^2}$

XZ² = XY² + YZ²

37² = 12² + YZ²

1369 = 144 + YZ²

1369 - 144 = YZ²

1225 = YZ²

$\sqrt{1225}$ = YZ

35 = YZ

Length of YZ = 35 m

Answer 2

Answer:

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