Question

find the perimeter of rectangle whose one side measure 10 metre and the diagonal is 26 metre​

Answer 1

$\underline{\underline{\sf{\maltese\:\:Question}}}$

• Find the Perimeter of a Rectangle whose One side measures 10 meter and Length of Diagonal is 26 meter

$\underline{\underline{\sf{\maltese\:\:Given}}}$

• One side measure = 10 meter

• Length of diagonal = 26 meter

$\underline{\underline{\sf{\maltese\:\:To\:Find}}}$

• Perimeter of Rectangle

$\underline{\underline{\sf{\maltese\:\:Answer}}}$

• Perimeter of Given Rectangle is 68 m

$\underline{\underline{\sf{\maltese\:\:Calculations}}}$

• Basic Terms before Going into Calculations:

Rectangle : A rectangle is a 4 sided simple closed figure having opposite sides equal. Diagonals are equal and bisect each other in a Rectangle.

Diagonal : Straight Line joining two opposite corners of a square, rectangle, or other straight-sided shape.

Hypotenuse : Longest side of a right-angled triangle, and the side opposite to Right angle

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We know : A rectangle can be divided into half forming 2 right angled triangles (90° angle Triangle)

• Consider A Rectangle "MNOP"

Where : OP is One Side and ON is the Diagonal

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,2.74){\framebox(0.25,0.25)}\put(4.74,0.01){\framebox(0.25,0.25)}\put(2,-0.7){\sf\large 10 m}\put(-0.5,-0.4){\bf O}\put(-0.5,3.2){\bf M}\put(5.3,-0.4){\bf P}\put(5.3,3.2){\bf N}\qbezier(0,0)(0,0)(5,3)\put(1.65,1.8){\sf\large 26 m}\end{picture}$

We get Use of Pythagoras Theorem Now :

• In A Right Angled Triangle (Hypotenuse)² = (Base)² + (Height)²  

From This Theorem we get :

⇒ (ON)² = (OP)² + (NP)²

⇒ (26 m)² = (10 m)² + (NP)²

⇒ 676 m² = 100 m² + (NP)²

• Subtracting 100 m² from Both Sides

⇒ 676 m² - 100 m² = (NP)²

⇒ 576 m² = (NP)²

• Taking Root on Both Sides

⇒ √(576 m²) = √(NP)²

⇒ 24 m = NP

• Switch Sides

⇒ NP = 24 m

Refer to this Diagram Now (Considering NP = y cm)

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 10 cm}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large y cm}\put(-0.5,-0.4){\bf O}\put(-0.5,3.2){\bf M}\put(5.3,-0.4){\bf P}\put(5.3,3.2){\bf N}\end{picture}$

Perimeter : Perimeter is the distance around the edge of a shape or the Length of outline of a shape

• For A Rectangle Perimeter is given by : 2 × (Length + Breadth)

⇒ Perimeter of Rectangle MNOP = 2 × (Length + Breadth)

⇒ Perimeter of Rectangle MNOP = 2 × (24 m + 10 m)

⇒ Perimeter of Rectangle MNOP = 2 × (34 m)

⇒ Perimeter of Rectangle MNOP =  68 m

∴ Perimeter of Given Rectangle is 68 m

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