Question

If the length and diagonal of a rectangle are 143m and 145m,find its area.

Answer 1

Answer:

the answer is in the pic ..

Answer 2

Step-by-step explanation:

$\underline{\underline{\maltese\: \: \textbf{\textsf{Question}}}}$

• If the length and diagonal of a rectangle are 143m and 145m, find its area.

$\underline{\underline{\maltese\: \: \textbf{\textsf{Answer}}}}$

• The area of the rectangle whose length and diagonal are 143m and 145m = 3432m².

$\underline{\underline{\maltese\: \: \textbf{\textsf{Given}}}}$

• Length of the rectangle = 143m.
• Diagonal of the rectangle = 145m.

$\underline{\underline{\maltese\: \: \textbf{\textsf{To\ Find}}}}$

• We have to find the area of rectangle.

$\underline{\underline{\maltese\: \: \textbf{\textsf{Basic\ Terms}}}}$

• Rectangle : A rectangle is a 2D shape in geometry, having 4 sides and 4 corners.
• Length : Length is a measure of how long an object is or the distance between two points.
• Breadth : Breadth is the width of a shape and describes the distance from the right side to the left side of a shape. 
• Area : In geometry, the area can be defined as the space occupied by a flat shape or the surface of an object.

$\underline{\underline{\maltese\: \: \textbf{\textsf{Formula\ Used}}}}$

• Pythagoras theorem = (Perpendicular)² + (Base)² = (Hypotenuse)².
• Area of rectangle = Length × Breadth.

$\underline{\underline{\maltese\: \: \textbf{\textsf{Solution}}}}$

➤ As we asked to find out the area of the rectangle. Length of the rectangle is given, then we need to find out the measure of its breadth.

➠ Through the given data, we make a diagram of a rectangle as OKAY with length of 143m and diagonal of 145m. By viewing the diagonal of rectangle along with length and breadth, we notice that a right angled triangle formed as KAY, where,

• KY = Diagonal = Hypotenuse = 145m.
• YA = Length = Base = 143m.
• KA = Breadth = Perpendicular = ?

➤ So now, by using the Pythagoras Theorem we will find out the breadth of rectangle.

$\underline{\underline{\maltese\: \: \textbf{\textsf{Calculations}}}}$

$\sf \rightarrow {(Perpendicular)^2\ +\ (Base)^2\ =\ (Hypotenuse)^2}$

• On substituting the values :-

$\sf \rightarrow {(KA)^2\ +\ (YA)^2\ =\ (KY)^2}$

• Here, YA = 143 and KY = 145.

$\sf \rightarrow {(KA)^2\ +\ (143)^2\ =\ (145)^2}$

$\sf \rightarrow {(KA)^2\ +\ 20449\ =\ 21025}$

$\sf \rightarrow {(KA)^2\ =\ 21025\ -\ 20449}$

$\sf \rightarrow {(KA)^2\ =\ 576}$

$\sf \rightarrow {KA\ =\ \sqrt{576}}$

${\therefore{\underline{\boxed{\sf {KA\ =\ 24m.}}}}}$

★ Since, we know that the measure of base perpendicular equals to the measure of breadth. Therefore, the breadth of the rectangle is 24m. So now, we have the length and the breadth of rectangle as 143m and 24m.

➤ So now, we will find out the area of rectangle by using the measures.

$\sf \rightarrow {Area\ of\ rectangle\ =\ length \times breadth}$

• On substituting the values :-

$\sf \rightarrow {Area\ of\ rectangle\ =\ 143m \times 24m}$

${\therefore{\underline{\boxed{\sf {Area\ of\ rectangle\ =\ 3432m^2.}}}}}$

• On solving the question, firstly we get the breadth of the rectangle. After having the breadth, we apply the values of length and breadth of rectangle in the formula of area of rectangle and find the area as 3432m².