Question

construct the following special quadrilaterals

a)construct a rectangle whose one side is 3 cm and one diagonal is equal to 5 cm.

b) construct a square having each diagonal 5 cm long.

pls draw in a paper and answer....
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Answer 1

Question :

a) Construct a rectangle whose one side is 3cm and one diagonal is equal to 5cm.

Answer :

(Please see the attachments carefully).

And as you said that you don't about Pythagoran theorem . Let me explain it to you.

Knowing this theorem is very important to solve this tye of questions .

Pythagoran Theorem:

This theorem is also known as Pythagoras theorem.

This theorem actually states that;

" Sum of the squares of sides of the right-angled triangle is equal to the square of the hypotenuse"

For example:

Let's consider a right angled triangleABC where

AB = a units , AC = b units , BC = c units.

( Tip : The side opposite to the right angle is known as the hypotenuse)

So, According to pythagoran theorem we get

$(side {)}^{2} + (side {)}^{2} = (hypotenuse {)}^{2}$

$(AB{)}^{2}+(AC{)}^{2}=(BC{)}^{2}$

$(a {)}^{2} + (b {)}^{2} = (c {)}^{2} \\ {a}^{2} + {b}^{2} = {c}^{2}$

This meant by Pythagoras theorem.

Now coming to the question,

We were given that one side is 3 cm and diagonal is 5cm.

So as we know that if we draw a diagonal in a rectangle it divides the rectangle into two right angled triangles.

Hence , we can find the measure of other side using the pythagoran theorem.

Here the diagonal becomes the hypotenuse.

So,

$(3 {)}^{2} + (x {)}^{2} = (5 {)}^{2} \\ 9 + {x}^{2} = 25 \\ {x}^{2} = 25 - 9 \\ {x}^{2} = 16 \\ x = \sqrt{16} \\ x = 4$

So here we got to know about the measure ofthe third side i.e. 4 cm

Now by using the properties of the rectangle that is

Opposite sides are equal.

We can complete the whole geometrical construction.

Question :

b) Construct a square having each diagonal 5cm long

Solution:

As we are familiar with the properties of the square that is

All sides are equal.

Here, we are going to use this property to solve this problem.

This sum also requires pythagoran theorem.

so,

Let the measure of the two sides be " x " cm.

and measurement of the hypotenuse is given that is 5cm ( diagonal ).

Hence,

$(x {)}^{2} + (x {)}^{2} = (5 {)}^{2} \\ {x}^{2} + {x}^{2} = 25 \\ 2 {x}^{2} = 25 \\ {x}^{2} = \frac{25}{2} \\ {x}^{2} = 12.5 \\ x = \sqrt{12.5} \\ x = 3.5355 - - - \\ so \: x = 3.5 \: cm$

Therefore,

The measurements of the sides of the square are 3.5 cm

Hence, using this measurements we can Construct the required square diagram.