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Find the value of "x" from the given figure...

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Find the value of "x" from the given figure... .................... ​-example-1
User Whoan
by
8.8k points

2 Answers

3 votes

Answer:

21 cm

Explanation:

Let M be the point of intersection of the diagonals AD and BC.


\implies x=\sf AD=AM+MD

As ΔAMD and ΔBMD are right triangles, use Pythagoras Theorem to work out the lengths of AM and MD.

Pythagoras Theorem


a^2+b^2=c^2

where:

  • a and b are the legs of the right triangle.
  • c is the hypotenuse (longest side) of the right triangle.


\begin{aligned}\implies \sf BM^2+AM^2 & =\sf AB^2\\\sf 8^2+AM^2 & = \sf 10^2\\\sf 64+AM^2 & = \sf 100\\\sf AM^2 & = \sf 100-64\\\sf AM^2 & = \sf 36\\\sf AM & = \sf √(36)\\\sf AM & = \sf 6\:\: cm\end{aligned}


\begin{aligned}\implies \sf BM^2+MD^2 & =\sf BD^2\\\sf 8^2+MD^2 & = \sf 17^2\\\sf 64+MD^2 & = \sf 289\\\sf MD^2 & = \sf 289-64\\\sf MD^2 & = \sf 225\\\sf MD& = \sf √(225)\\\sf MD& = \sf 15\:\: cm\end{aligned}

Therefore:


\begin{aligned}\implies x & =\sf AM+MD\\x & = \sf 6+15\\x & = \sf 21\:\:cm\end{aligned}

So the value of
x from the given figure is 21 cm.

User Gourango Sutradhar
by
8.4k points
3 votes

Answer:

x = 21 cm

Explanation:

is a rhombus formed by 4 right triangles, let's consider the small / large couple

the triangle at the top and the triangle at the bottom are rectangles

we can solve with the Pythagorean theorem.

  • we find the side (cathetus) of the small one

c² = 10² - 8²

c² = 100 - 64

c² = 36

c = √36

c = 6 cm

  • we find the side (cathetus) of the largest

c² = 17² - 8²

c² = 289 - 64

c² = 225

c = √225

c = 15 cm

  • now we add the results and we have x

6 + 15 =

21cm

User Anjani Barnwal
by
8.4k points

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