if the diagonal and area of a rectangle are 25 m and 168 m square respectively. what is the length of the rectangle
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Let the length of rectangle is l m and breadth of rectangle is b m,
As all vertex angles of a rectangle are right angles, applying Pythagoras Theorem,
Diagonal of rectangle = √{ l² + b² }
In the question, diagonal of rectangle = 25 m
Comparing both the values of the diagonal,
25 m = √{ l² m² + b² m² }
( 25 m )² = l² m² + b² m²
625m² = l² m² + b² m²
625 m² - b² m² = l² m²
√{ 625 m² - b² m² ) = l m
Area of rectangle = l × b
In the question, area of rectangle = 168 m
Comparing both the values of the area,
.
168 m² = l m × b m
From the above explanation we can write the value of l which is √{ 625 m² - b² m² } ,
185 m² = √{ 625 m² - b² m² } × b m
185 m² = √{ 625 - b² } m × b m
185 m² = √{ 625 - b² } × b m²
185 = √{ 625 - b² } × b
34225 = { 625 - b² } × b
34225 = 625b² - b⁴
b⁴ - 625b² + 34225 = 0
Let b² = x
x² - 625x + 34225 = 0
By applying quadratic formula,
So,
On putting approximate values of roots, we get that value b is 7.78745 or 23.75617
Hence,
b m = Breadth of rectangle = 7.78745 or
23.75617
l m = length of rectangle = √{ 625 m² - ( b )² m² } = √{ 625 m² - ( 7.78745 )² m² } or √{ 625 m² - ( 23.75617 )² } = 23.75617 or 7.78745 respectively and respective to the Breadth.
Answer : length of rectangle = 23.75617 or 7.78745
As all vertex angles of a rectangle are right angles, applying Pythagoras Theorem,
Diagonal of rectangle = √{ l² + b² }
In the question, diagonal of rectangle = 25 m
Comparing both the values of the diagonal,
25 m = √{ l² m² + b² m² }
( 25 m )² = l² m² + b² m²
625m² = l² m² + b² m²
625 m² - b² m² = l² m²
√{ 625 m² - b² m² ) = l m
Area of rectangle = l × b
In the question, area of rectangle = 168 m
Comparing both the values of the area,
.
168 m² = l m × b m
From the above explanation we can write the value of l which is √{ 625 m² - b² m² } ,
185 m² = √{ 625 m² - b² m² } × b m
185 m² = √{ 625 - b² } m × b m
185 m² = √{ 625 - b² } × b m²
185 = √{ 625 - b² } × b
34225 = { 625 - b² } × b
34225 = 625b² - b⁴
b⁴ - 625b² + 34225 = 0
Let b² = x
x² - 625x + 34225 = 0
By applying quadratic formula,
So,
On putting approximate values of roots, we get that value b is 7.78745 or 23.75617
Hence,
b m = Breadth of rectangle = 7.78745 or
23.75617
l m = length of rectangle = √{ 625 m² - ( b )² m² } = √{ 625 m² - ( 7.78745 )² m² } or √{ 625 m² - ( 23.75617 )² } = 23.75617 or 7.78745 respectively and respective to the Breadth.
Answer : length of rectangle = 23.75617 or 7.78745
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