1.

A right triangle when one side is 3.5cm and sum of other sides and the hypotenuse is 5.5cm.

Answer»

Solution :Let given right triangle be `ABC` .
Then , given `BC` = `3.5cm angleB = 90^(@)` and SUM of other side and hypotenuse i.e., `AB + AC = 5.5cm`
To construct `DeltaABC` use the following STEPS
(i) Draw the base `BC = 3.5cm`
(ii) Make an angle `XBC` = `90^(@)` at the point `B` of base `BC`.
(III) Cut the line segment BD EQUAL to `AB+ AC` i.e., `5.5cm` from the ray XB.
(iv) Join DC and make an `angleDCY` equal to `angleBDC` .
Let Y intersect BX at A.
Thus , `DeltaABC` is the required triangle.
Justification
Base BC and `angleB` are drawn as given.
In `DeltaACD, angle ACD = ANGLEADC` [by construction]
`:.` AD = AC...(i) [sides opposite to equal angle are equal]
Now `AB = BD - AD = BD- AC`[from Eq. (i)]
`rArr BD = AB + AC`
Thus , our construction is justified.


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