Question

Find the perimeter of the rectangle whose length is 15 cm and a diagonal is 17 cm.​

Answer 1

Step-by-step explanation:

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

• Find the perimeter of the rectangle whose length is 15cm and a diagonal is 17cm.

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

• The perimeter of the rectangle = 46cm.

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

• Length of the rectangle = 15cm.
• Diagonal of the rectangle = 17cm.

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

• We have to find out the perimeter of the 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.
• Perimeter : Perimeter is the distance around a two-dimensional shape. 

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

• Pythagoras theorem :- (Diagonal)² = (Breadth)² + (Length)².
• Perimeter of rectangle = 2(Length + Breadth).

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

➤ As we are asked to find the perimeter of the rectangle. Length and diagonal 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 ABCD with length of 15cm and diagonal of 17cm. By viewing the diagonal of rectangle along with length and breadth, we notice that a right angled triangle formed as BCD, where,

• BD = Diagonal = Hypotenuse = 17cm.
• DC = Length = Base = 15cm.
• BC = Breadth = Perpendicular = ?

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

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

$\begin{gathered}\orange\bigstar\: {\Large\mid}\: \bf{(Diagonal)^2\ =\ (Breadth)^2\ +\ (Length)^2}\: {\Large\mid}\: \green\bigstar \end{gathered}$

• On substituting the values :-

$\sf \dashrightarrow {(BD)^2\ =\ (BC)^2\ +\ (DC)^2}$

• Here, BD = 17 and DC = 15.

$\sf \dashrightarrow {(17)^2\ =\ (BC)^2\ +\ (15)^2}$

$\sf \dashrightarrow {289\ =\ (BC)^2\ +\ 225}$

$\sf \dashrightarrow {(BC)^2\ =\ 289\ -\ 225}$

$\sf \dashrightarrow {(BC)^2\ =\ 64}$

$\sf \dashrightarrow {BC\ =\ \sqrt{64}}$

${\therefore{\underline{\boxed{\sf {BC\ =\ 8cm.}}}}}$

★ Since, we know that the measure of base perpendicular equals to the measure of breadth. Therefore, breadth of the rectangle is 8cm. So now, we have the length and breadth of rectangle as 15cm and 8cm.

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

$\begin{gathered}\orange\bigstar\: {\Large\mid}\: \bf{Perimeter\ of\ rectangle\ =\ 2(Length\ +\ Breadth)}\: {\Large\mid}\: \green\bigstar \end{gathered}$

• On substituting the values :-

$\sf \dashrightarrow {Perimeter\ of\ rectangle\ =\ 2(15\ +\ 8)}$

$\sf \dashrightarrow {Perimeter\ of\ rectangle\ =\ 2(23)}$

$\sf \dashrightarrow {Perimeter\ of\ rectangle\ =\ 2 \times 23}$

${\therefore{\underline{\boxed{\sf {Perimeter\ of\ rectangle\ =\ 46cm.}}}}}$

• On solving the question, firstly we get the breadth of the rectangle. After that, by applying the measures in the formula of perimeter of rectangle we get the perimeter as 46cm.

Answer 2

Refer to the attachment!